1M 



ALEXANDRINE VKRSE. 



ALOEBKA. 



Library u said to have Amounted to 700,000 volume*. But the rolls 

 (nJAmiim) spoken of cunUinod fur Ion than a printed volume ; , (or 

 iiwUncc, the Mctamorphom ' of Ovid, in tift.t-n book*, would make 

 fifteen volumes. This oooadernti-m will bring th<- uuuiU-r of books 

 n ilhin the bound* of credibility. 



After the capture of Alexandria by Juliui Cesar * Urge part .-i the 

 library WM burnt. CiibK.n (chap, xxviii.) assert* that the old library 

 was totally consumed, and that the oolUx-tion fim Porgainiui. whieh 

 wan presented by Marcus Antoniim through Cleopatra, was tho founda- 

 li.-n f tin- new one, which continued to increaw in size and rapuMloa 

 f.. r four .vntmiwt, until, at the destruction of the Serapeion l>y 

 Theophilus, patriarch of Alexandria, it was dispersed, X.D. 390. Still 

 tin- library was re-established ; and Alexandria continued to flourish 

 . -f ihr ehief seats of literature till it was conquered by the Arab* 

 in 640. Tin- library wan then burnt, according to the story generally 

 I* lit Mil. in eounequence of the fanatic decision of the Khalif Omar, 

 If these writing! of the Greek* agree with the Book of God, they are 

 useless, and need not be _ preserved : if they disagree, they Are per- 

 nil-ion*, and ought to be destroyed." Accordingly, it is said, they were 

 mpl'-\id to heat the 4000 baths of the city ; and such was their niini- 

 1-1 . tli.it six months were barely sufficient for the consumption of thin 

 precious fuel. (Gibbon, chap, li.) i;iiil>ii ha* employed his ingenuity 

 to discredit this account, which in itself appears by no means impro- 

 bable. The library was at all events dispersed, if not destroyed ; it 

 ceased to exist as a public institution. 



Connected with the library of Brucheiou waa a college, or retreat 

 for learned men, called the Museum, where they were maintained at 

 tli.- public expense, in unbroken leisure, and with every facility for the 

 pursuit of knowledge. This establishment was subsequently transferred 

 to the Serapeion, and continued to flourish till the destruction of the 

 U-inplo by Theophilus. The sciences of mathematics, astronomy, and 

 geography, were especially cultivated : witness the names of Euclid, 

 Apollouius, Eratosthenes ; and, in later times, of Ptolenucus the geo- 

 grapher. Criticism, philology, and antiquities, were also much studied. 

 i A i. t:\.vxOREiA, in GEOG. Div.J Alexandria continued, until its capture 

 by the Saracens, one of the most noted seats of learning in the world. 



(Afad. da Iiucriptiont, torn. ix. p. 397; Gibbon, chap, li., and the 

 original authorities quoted in these works.) 



ALEXANDRINE VERSE, a species of verse so called from having 

 been first employed, according to some authorities, in a French trans- 

 lation, by Alexander de Paris and Lambert Lieon, of a Latin poem 

 ealli-d the Alexandriad, according to others in an original work in the 

 former language, on the life of Alexander the Great, composed by these 

 poets in association with Jean le NiveloU and others. After its first 

 introduction, it appears to have fallen for a long time into di-u.-i- 

 among the French poets, until it was revived by Jean Antoine de Bccuf 

 (one of the seven called the Pleiades), in the reign of Francis I. The 

 first, however, who attuned the national ear of France to this verse, 

 was the celebrated Ronsard, since whose time it has become the regular 

 heroic verse of the French language : or that in which all their epic, 

 tragic, and other greater poetical works ore composed. It consists of 

 twelve syllables, subject to the rule that it shall always be broken into 

 two regular hemistichs, or, in other words, that its sixth syllable shall 

 always terminate a word. The English Alexandrine verse consists in 

 like manner of twelve syllables ; but among us it has been rarely used 

 throughout a whole poem. The longest and most remarkable poetical 

 work in our language, written wholly in Alexandrine verse, is Drayton's 

 ' Pplyolbiou.' In general, it is employed only occasionally in poems 

 written in our usual heroic verse of ten syllables, and never except in 

 the concluding line of the couplet or triplet. In Dryden, by whom it 

 has been used in this manner most frequently, and with the finest 

 effect, it most commonly winds up a triplet such as that in which 

 1'ope has at once described and exemplified the manner of his great 

 predecessor: 



" Waller was smooth ; but Dryden taught to join 

 The rarjring verse, the full rewuoding line, 

 The long majestic march, and energy divine." 



The Alexandrine verse in English also forum the closing line of what 

 Is called the Spenserian stanza. Regularly, it ought always, as in 

 French, to be divisible into two hrnmtichs ; but, in the freer spirit o: 

 our poetry, this rule is occasionally violated. 



ALGAROTH,orALGAROTTl,I'Ci\VDKU OK [ANTIMONY, Oxv 



I III.' 'HIM. OF.] 



ALGEBRA. This word is derived by contraction from the Arabic 

 phrase Aljelir t al tnotSbalak, the nearest English translation of whicl 

 U ratoratioH and rnlurtion. So short a definition is of course useless 

 we shall endeavour to give the first and most simple view of thii 

 science, our limits not permitting us to go, even in the smallest degree 

 into iU operations. 



In establishing the rules of arithmetic, it in always necessary to use 

 general reasoning : that is, reasoning the nature of whioh would not be 

 altered if other numbers had been chosen, different from tho- win. 1 

 were really employed in the question. For example, if 2 acre* let for 

 IS/., how ninth will 17 acres let for? It U shown immediately tha 

 the number of pound* required is that obtained by multiplying 13 and 

 17 together, ami dividing the pr.luc t l,y 2: and it appear* m 

 that, by the same reasoning, a similar rule might be established wh 



he numbers are different from thow given above. provided the form 

 of the question remain the same. That is, if any number of acres we 

 ilease to name, cost a certain numlx i of |.un<U. the priee > t am otln r 

 lumber of acres may be found by multiplying that other number by 

 the number of pounds the first acres cost, and dividing by the mimi-r 

 of the first-mentioned acres. Thus we have established a general rule, 

 and the steps by whioh we translate this into an algebraical expi 

 are as follows. Wo invent short signs, to signify that multipl 

 and division are to take place : we express tho former by putting X 

 jetween the numbers which are to be multiplied together, the l.ittfi- 

 py writing the divisor under the dividend, and drawing a line I 

 :hem. The foregoing rule then stands as follows : 



Price in poundi of ) . 

 second No. of acre*, f 



| 1'ricc In pounds of | 

 Second No. of acres x ( flnt No. of mcrei. ) 



Flrat No. of acre*. 



So far we have aMifeviaU-d by usiiif? two tt/niljvl* <if <i/x/-'iiV/ ; to 

 which we may add that we write + l>etw<vn two numbers whieh au- 

 to 1 p<; added together, and between tw< p numbers of whieh t he second 

 is to be taken away from the first. Now suppose that, to catch tli<- 

 M, we put a letter whenever a number is named in the question, in 

 order that by looking for that letter we may quiekly find out in what 

 part of the result the aforesaid number is used. For example : It a 

 certain number of acres (a) cost a certain number of pounds (M, how 

 many pounds will another number of acres cost (c) ? The anpv, 

 as above, 



X 



First No. of acre* (a) 



The last step is, to let the letters themselves stand for the .- 

 numbers, whioh will save the necessity of writing words in the result. 

 Our final algebraical way of writing the question will then be If 

 a acres cost 6 pounds, how much will c acres cost ? The answer u, 



c x 6 t 6 



- pounds, usually written pounds. 



To take another instance, which \ve first write algebraically: If 

 a pounds of sugar, at m pence a pound, be mixed with l> }><< 

 sugar, worth n pence a pound, the worth of a pound of the mixture is 



m o + n b 



which in the usual Language cannot be stated more shortly than as 

 follows : To find the worth of a pound of mixed sugar, knowing how 

 much of each sort was in the mixture, and how much each was worth 

 per pound, multiply the number of pounds of each sort by the uviml>er 

 of pence which a pound of it caste, add the products together, and 

 divide by the whole number of pounds in the mixture. 



This will be sufficient to give the reader an idea of the notation oi 1 

 algebra, and the very great abbreviation which it introduces into the 

 details of processes. For further explanations, see ADDITION'. &e., 

 POSITIVE, NEGATIVE, EQUALITY, EXPONENT, INDEX, POWER, ROOT, and 

 the article NOTATION. 



We have said nothing of the reasoning of algebra, because it differ.- 

 in no respect from that of arithmetic, or any other science, at least in 

 the elementary part. It proceeds upon such fundamental and self- 

 evident principles as the following : that two equal numbers remain 

 equal when the same number hits been added to or subtracted from 

 them, or when they have been both multiplied or both divided by the 

 same number that no number is altered by the addition of any number 

 followed by the subtraction of the same, or by being multiplied by ,,ny 

 number, if the product be afterwards divided by the same numK-r ; 

 and so on. To take a very simple case, suppose we ask, What numU -r 

 is that, which multiplied by 3 and the product increased by 6, gives 

 30 f Without knowing the number, we can see that if three times the 

 number, together with 6, gives 30, three times the number in 

 24, or the number required must be the third put o| _'!, or 8. The 

 algebraical method of expressing this is as follow.-, where =: mean.: 

 that the num)>orx lietween which it is placed are the 



Let x stand for the number ; then )py the question 



3 ., + 6 = 30 



Therefore 3* =30 = 24 

 2 



or x = lf= 8 



We give the preceding, not as a specimen of the advantages' of 

 algebra, but of its language only, for we have punxnely chosen suuli a 

 question as needs no assistance, in order to make the method of ex- 

 pression more evident. [AXIOM ; Egr ATION : PROBLEM.] 



The operations of algebra are to be considered in a very dillen-nt 

 light from those of arithmetic. In the latter science, absolute utnnln i , 

 are given, and an absolute numlper i nought : in the former it is 

 rather the nature of the question whieh is given, and it is required to 

 find, not DO much the answer to any particular cane, as a general method 

 of solving any case whatever. The symlpols used are not numbers, but 

 ' representations of them, that is letters, each of which may 



